Question

The first four terms of a quadratic sequence are 9, 23, 45 and 75 work out the next two terms of the sequence

Answer 1

9, 23, 45, 75, 113, 159

Explanation:

Quadratic Sequence

The difference between two consecutive terms of a quadratic sequence is another sequence, this one is an arithmetic sequence.

The first terms are given as:

9, 23, 45, 75, ...

Let's compute the differences:

23 - 9 = 14

45 - 23 = 22

75 - 45 = 30

Note the differences form an aritmetic sequence of commons difference 8.

The next two terms will be formed adding 8 to the previous difference, that is:

30 + 8 = 38 is the next difference. And the next term is

75 + 38 = 113

38 + 8 = 46 is the next difference, and the next term is

113 + 46 = 159

Thus, the complete sequence is

9, 23, 45, 75, 113, 159